.TH AT_PID "9" "2007-05-12" "LinuxCNC Documentation" "HAL Component"
.de TQ
.br
.ns
.TP \\$1
..

.SH NAME
at_pid \- proportional/integral/derivative controller with auto tuning
.SH SYNOPSIS
\fBloadrt at_pid [num_chan=\fInum\fB | names=\fIname1\fB[,\fIname2...\fB]]



.SH DESCRIPTION
\fBat_pid\fR is a classic Proportional/Integral/Derivative controller,
used to control position or speed feedback loops for servo motors and
other closed-loop applications.
.P
\fBat_pid\fR supports a maximum of sixteen controllers.  The number that
are actually loaded is set by the \fBnum_chan\fR argument when
the module is loaded.  Alternatively, specify \fBnames=\fR and unique names
separated by commas.
.P
The \fBnum_chan=\fR and \fBnames=\fR specifiers are mutually exclusive.
If neither \fBnum_chan=\fR nor \fBnames=\fR are specified, the default
value is three.
.P
If \fBdebug\fR is set to 1 (the default is 0), some
additional HAL parameters will be exported, which might be useful
for tuning, but are otherwise unnecessary.
.P
\fBat_pid\fR has a built in auto tune mode. It works by setting up a limit
cycle to characterize the process. From this, \fBPgain/Igain/Dgain\fR or
\fBPgain/Igain/FF1\fR can be determined using Ziegler-Nichols. When using
\fBFF1\fR, scaling must be set so that \fBoutput\fR is in user units per second.
.P
During auto tuning, the \fBcommand\fR input should not change. The limit
cycle is setup around the commanded position. No initial tuning values are
required to start auto tuning.  Only \fBtune\-cycles\fR, \fBtune\-effort\fR
and \fBtune\-mode\fR need be set before starting auto tuning.  When auto tuning
completes, the tuning parameters will be set. If running from LinuxCNC, the
FERROR setting for the axis being tuned may need to be loosened up as it must
be larger than the limit cycle amplitude in order to avoid a following error.
.P
To perform auto tuning, take the following steps.  Move the axis to be tuned,
to somewhere near the center of it's travel.  Set \fBtune\-cycles\fR (the
default value should be fine in most cases) and \fBtune\-mode\fR. Set
\fBtune\-effort\fR to a small value. Set \fBenable\fR to true. Set
\fBtune\-mode\fR to true. Set \fBtune\-start\fR to true. If no oscillation
occurs, or the oscillation is too small, slowly increase \fBtune\-effort\fR.
Auto tuning can be aborted at any time by setting \fBenable\fR or
\fBtune\-mode\fR to false.

.SH NAMING
The names for pins, parameters, and functions are prefixed as:
  \fBpid.N.\fR for N=0,1,...,num\-1 when using \fBnum_chan=num\fR
  \fBnameN.\fR for nameN=name1,name2,... when using \fBnames=name1,name2,...\fR

The \fBpid.N.\fR format is shown in the following descriptions.


.SH FUNCTIONS
.TP 
\fBpid.\fIN\fB.do\-pid\-calcs\fR (uses floating-point)
Does the PID calculations for control loop \fIN\fR.

.SH PINS

.TP
\fBpid.\fIN\fB.command\fR float in
The desired (commanded) value for the control loop.
.TP
\fBpid.\fIN\fB.feedback\fR float in
The actual (feedback) value, from some sensor such as an encoder.
.TP
\fBpid.\fIN\fB.error\fR float out
The difference between command and feedback.
.TP
\fBpid.\fIN\fB.output\fR float out
The output of the PID loop, which goes to some actuator such as a motor.
.TP
\fBpid.\fIN\fB.enable\fR bit in
When true, enables the PID calculations.  When false, \fBoutput\fR is zero,
and all internal integrators, etc, are reset.
.TP
\fBpid.\fIN\fB.tune\-mode\fR bit in
When true, enables auto tune mode.  When false, normal PID calculations are
performed.
.TP
\fBpid.\fIN\fB.tune\-start\fR bit io
When set to true, starts auto tuning.  Cleared when the auto tuning completes.

.SH PARAMETERS
.TP
\fBpid.\fIN\fB.Pgain\fR float rw
Proportional gain.  Results in a contribution to the output that is the error
multiplied by \fBPgain\fR.
.TP
\fBpid.\fIN\fB.Igain\fR float rw
Integral gain.  Results in a contribution to the output that is the integral
of the error multiplied by \fBIgain\fR.  For example an error of 0.02 that
lasted 10 seconds would result in an integrated error (\fBerrorI\fR) of 0.2,
and if \fBIgain\fR is 20, the integral term would add 4.0 to the output.
.TP
\fBpid.\fIN\fB.Dgain\fR float rw
Derivative gain.  Results in a contribution to the output that is the rate of
change (derivative) of the error multiplied by \fBDgain\fR.  For example an
error that changed from 0.02 to 0.03 over 0.2 seconds would result in an error
derivative (\fBerrorD\fR) of of 0.05, and if \fBDgain\fR is 5, the derivative
term would add 0.25 to the output.
.TP
\fBpid.\fIN\fB.bias\fR float rw
\fBbias\fR is a constant amount that is added to the output.  In most cases
it should be left at zero.  However, it can sometimes be useful to compensate
for offsets in servo amplifiers, or to balance the weight of an object that
moves vertically. \fBbias\fR is turned off when the PID loop is disabled,
just like all other components of the output.  If a non-zero output is needed
even when the PID loop is disabled, it should be added with an external HAL
sum2 block.
.TP
\fBpid.\fIN\fB.FF0\fR float rw
Zero order feed-forward term.  Produces a contribution to the output that is
\fBFF0\fR multiplied by the commanded value.  For position loops, it should
usually be left at zero.  For velocity loops, \fBFF0\fR can compensate for
friction or motor counter-EMF and may permit better tuning if used properly.
.TP
\fBpid.\fIN\fB.FF1\fR float rw
First order feed-forward term.  Produces a contribution to the output that
\fBFF1\fR multiplied by the derivative of the commanded value.  For
position loops, the contribution is proportional to speed, and can be used
to compensate for friction or motor CEMF.  For velocity loops, it is
proportional to acceleration and can compensate for inertia.  In both
cases, it can result in better tuning if used properly.
.TP
\fBpid.\fIN\fB.FF2\fR float rw
Second order feed-forward term.  Produces a contribution to the output that is
\fBFF2\fR multiplied by the second derivative of the commanded value.  For
position loops, the contribution is proportional to acceleration, and can be
used to compensate for inertia.  For velocity loops, it should usually be
left at zero.
.TP
\fBpid.\fIN\fB.deadband\fR float rw
Defines a range of "acceptable" error.  If the absolute value of \fBerror\fR
is less than \fBdeadband\fR, it will be treated as if the error is zero.
When using feedback devices such as encoders that are inherently quantized,
the deadband should be set slightly more than one-half count, to prevent
the control loop from hunting back and forth if the command is between two
adjacent encoder values.  When the absolute value of the error is greater
than the deadband, the deadband value is subtracted from the error before
performing the loop calculations, to prevent a step in the transfer function
at the edge of the deadband.  (See \fBBUGS\fR.)
.TP
\fBpid.\fIN\fB.maxoutput\fR float rw
Output limit.  The absolute value of the output will not be permitted
to exceed \fBmaxoutput\fR, unless \fBmaxoutput\fR is zero.  When the output
is limited, the error integrator will hold instead of integrating, to prevent
windup and overshoot.
.TP
\fBpid.\fIN\fB.maxerror\fR float rw
Limit on the internal error variable used for P, I, and D.  Can be used to
prevent high \fBPgain\fR values from generating large outputs under conditions
when the error is large (for example, when the command makes a step change).
Not normally needed, but can be useful when tuning non-linear systems.
.TP
\fBpid.\fIN\fB.maxerrorD\fR float rw
Limit on the error derivative.  The rate of change of error used by the
\fBDgain\fR term will be limited to this value, unless the value is
zero.  Can be used to limit the effect of \fBDgain\fR and prevent large
output spikes due to steps on the command and/or feedback.  Not normally
needed.
.TP
\fBpid.\fIN\fB.maxerrorI\fR float rw
Limit on error integrator.  The error integrator used by the \fBIgain\fR
term will be limited to this value, unless it is zero.  Can be used to prevent
integrator windup and the resulting overshoot during/after sustained errors.
Not normally needed.
.TP
\fBpid.\fIN\fB.maxcmdD\fR float rw
Limit on command derivative.  The command derivative used by \fBFF1\fR will
be limited to this value, unless the value is zero.  Can be used to prevent
\fBFF1\fR from producing large output spikes if there is a step change on the
command.  Not normally needed.
.TP
\fBpid.\fIN\fB.maxcmdDD\fR float rw
Limit on command second derivative.  The command second derivative used by
\fBFF2\fR will be limited to this value, unless the value is zero.  Can be
used to prevent \fBFF2\fR from producing large output spikes if there is a
step change on the command.  Not normally needed.
.TP
\fBpid.\fIN\fB.tune\-type\fR u32 rw
When set to 0, \fBPgain/Igain/Dgain\fR are caclulated. When set to 1,
\fBPgain/Igain/FF1\fR are calculated.
.TP
\fBpid.\fIN\fB.tune\-cycles\fR u32 rw
Determines the number of cycles to run to characterize the process.
\fBtune\-cycles\fR actually sets the number of half cycles. More cycles results
in a more accurate characterization as the average of all cycles is used.
.TP
\fBpid.\fIN\fB.tune\-effort\fR float rw
Determines the effor used in setting up the limit cycle in the process.
\fBtune\-effort\fR should be set to a positive value less than \fBmaxoutput\fR.
Start with something small and work up to a value that results in a good
portion of the maximum motor current being used. The smaller the value, the
smaller the amplitude of the limit cycle.
.TP
\fBpid.\fIN\fB.errorI\fR float ro (only if debug=1)
Integral of error.  This is the value that is multiplied by \fBIgain\fR to produce the Integral term of the output.
.TP
\fBpid.\fIN\fB.errorD\fR float ro (only if debug=1)
Derivative of error.  This is the value that is multiplied by \fBDgain\fR to produce the Derivative term of the output.
.TP
\fBpid.\fIN\fB.commandD\fR float ro (only if debug=1)
Derivative of command.  This is the value that is multiplied by \fBFF1\fR to produce the first order feed-forward term of the output.
.TP
\fBpid.\fIN\fB.commandDD\fR float ro (only if debug=1)
Second derivative of command.  This is the value that is multiplied by
\fBFF2\fR to produce the second order feed-forward term of the output.
.TP
\fBpid.\fIN\fB.ultimate\-gain\fR float ro (only if debug=1)
Determined from process characterization. \fBultimate\-gain\fR is the ratio of
\fBtune\-effort\fR to the limit cycle amplitude multiplied by 4.0 divided by Pi.
\fBpid.\fIN\fB.ultimate\-period\fR float ro (only if debug=1)
Determined from process characterization. \fBultimate\-period\fR is the period
of the limit cycle.

.SH BUGS
Some people would argue that deadband should be implemented such that error is
treated as zero if it is within the deadband, and be unmodified if it is outside
the deadband.  This was not done because it would cause a step in the transfer
function equal to the size of the deadband.  People who prefer that behavior are
welcome to add a parameter that will change the behavior, or to write their own
version of \fBat_pid\fR. However, the default behavior should not be changed.
